Suppose that a number x is to be selected from the real line R, and let A, B, and C be the events represented by the following subsets of R, where the notation {x : −−−} denotes the set containing every point x for which the property presented following the colon is satisfied: A = {x : 1 ≤ x ≤ 5} B = {x : 3 < x ≤ 7} C = {x : x ≤ 0} Problems: 1.2) Toss a coin 4 times. Let A denote the event that a head is obtained on the first toss, and let B denote the event that a head is obtained on the fourth toss. Is A ∩ B empty?
Suppose that a number x is to be selected from the real line R, and let A, B, and C be the events
represented by the following subsets of R, where the notation {x : −−−} denotes the set containing
every point x for which the property presented following the colon is satisfied:
A = {x : 1 ≤ x ≤ 5}
B = {x : 3 < x ≤ 7}
C = {x : x ≤ 0}
Problems:
1.2) Toss a coin 4 times. Let A denote the
1.3) Consider rolling a six-sided die once. Let A be the set of outcomes where an odd number comes up. Let B be the set of outcomes where a 1 or a 2 comes up. Calculate the sets on both sides of the equalities (Ac ∩ Bc) c = A ∪ B and (Ac ∪ Bc ) c = A ∩ B and verify that the equalities hold.
1.4) We are given that P(A) = 0.55, P(B) = 0.35, and P(A∪B) = 0.75. Determine P(Ac ) and P(A∩B).
1.5) Out of the students in a class, 60% are geniuses, 70% love chocolate and 40% fall into both categories. Determine the probability that a randomly selected student is neither a genius nor a chocolate lover.
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